Universal families for conull FK spaces

Author:
A. K. Snyder

Journal:
Trans. Amer. Math. Soc. **284** (1984), 389-399

MSC:
Primary 46A45; Secondary 40H05

MathSciNet review:
742431

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Abstract: This paper considers the problem of determining a useful family of sequence spaces which is universal for conull FK spaces in the following sense: An FK space is conull if and only if it contains a member of the family. In the equivalent context of weak wedge spaces, an appropriate family of subspaces of boundedness domains of matrices is shown to be universal. Most useful is the fact that the members of this family exhibit unconditional sectional convergence. The latter phenomenon is known for wedge spaces. Another family of spaces which is universal for conull spaces among semiconservative spaces is provided. The spaces are designed to simplify gliding humps arguments. Improvements are thereby obtained for some pseudoconull type theorems of Bennett and Kalton. Finally, it is shown that conull spaces must contain pseudoconull BK algebras.

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DOI:
https://doi.org/10.1090/S0002-9947-1984-0742431-1

Keywords:
FK space,
conull,
weak wedge

Article copyright:
© Copyright 1984
American Mathematical Society